LaTeX to CAS translator
This mockup demonstrates the concept of TeX to Computer Algebra System (CAS) conversion.
The demo-application converts LaTeX functions which directly translate to CAS counterparts.
Functions without explicit CAS support are available for translation via a DRMF package (under development).
The following LaTeX input ...
{\displaystyle \operatorname{li}(x) = \int_0^x \frac{dt}{\ln t}. }
... is translated to the CAS output ...
Semantic latex: \logint@{x} = \int_0^x \frac{\diff{t}}{\ln t}
Confidence: 0.89530287320794
Mathematica
Translation: LogIntegral[x] == Integrate[Divide[1,Log[t]], {t, 0, x}, GenerateConditions->None]
Information
Sub Equations
- LogIntegral[x] = Integrate[Divide[1,Log[t]], {t, 0, x}, GenerateConditions->None]
Free variables
- x
Symbol info
- Logarithmic integral; Example: \logint@{x}
Will be translated to: LogIntegral[$0] Constraints: x > 1 Mathematica uses other branch cuts: (-\inf, 1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/6.2#E8 Mathematica: https://reference.wolfram.com/language/ref/LogIntegral.html
- Natural logarithm; Example: \ln@@{z}
Will be translated to: Log[$0] Constraints: z != 0 Branch Cuts: (-\infty, 0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.2#E2 Mathematica: https://reference.wolfram.com/language/ref/Log.html
Tests
Symbolic
Test expression: (LogIntegral[x])-(Integrate[Divide[1,Log[t]], {t, 0, x}, GenerateConditions->None])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \logint [\logint]
Tests
Symbolic
Numeric
Maple
Translation: Li(x) = int((1)/(ln(t)), t = 0..x)
Information
Sub Equations
- Li(x) = int((1)/(ln(t)), t = 0..x)
Free variables
- x
Symbol info
- Logarithmic integral; Example: \logint@{x}
Will be translated to: Li($0) Constraints: x > 1 Relevant links to definitions: DLMF: http://dlmf.nist.gov/6.2#E8 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=Li
- Natural logarithm; Example: \ln@@{z}
Will be translated to: ln($0) Constraints: z != 0 Branch Cuts: (-\infty, 0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.2#E2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=ln
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- integral representation
- positive real number
- logarithmic integral
Complete translation information:
{
"id" : "FORMULA_0dcdda66ab1f2d188cebaab11ddd8c9b",
"formula" : "\\operatorname{li}(x) = \\int_0^x \\frac{dt}{\\ln t}",
"semanticFormula" : "\\logint@{x} = \\int_0^x \\frac{\\diff{t}}{\\ln t}",
"confidence" : 0.8953028732079359,
"translations" : {
"Mathematica" : {
"translation" : "LogIntegral[x] == Integrate[Divide[1,Log[t]], {t, 0, x}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "LogIntegral[x] = Integrate[Divide[1,Log[t]], {t, 0, x}, GenerateConditions->None]" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"\\logint" : "Logarithmic integral; Example: \\logint@{x}\nWill be translated to: LogIntegral[$0]\nConstraints: x > 1\nMathematica uses other branch cuts: (-\\inf, 1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/6.2#E8\nMathematica: https://reference.wolfram.com/language/ref/LogIntegral.html",
"\\ln" : "Natural logarithm; Example: \\ln@@{z}\nWill be translated to: Log[$0]\nConstraints: z != 0\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.2#E2\nMathematica: https://reference.wolfram.com/language/ref/Log.html"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "ERROR",
"numberOfTests" : 1,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 1,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "LogIntegral[x]",
"rhs" : "Integrate[Divide[1,Log[t]], {t, 0, x}, GenerateConditions->None]",
"testExpression" : "(LogIntegral[x])-(Integrate[Divide[1,Log[t]], {t, 0, x}, GenerateConditions->None])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\logint [\\logint]"
}
}
},
"Maple" : {
"translation" : "Li(x) = int((1)/(ln(t)), t = 0..x)",
"translationInformation" : {
"subEquations" : [ "Li(x) = int((1)/(ln(t)), t = 0..x)" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"\\logint" : "Logarithmic integral; Example: \\logint@{x}\nWill be translated to: Li($0)\nConstraints: x > 1\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/6.2#E8\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=Li",
"\\ln" : "Natural logarithm; Example: \\ln@@{z}\nWill be translated to: ln($0)\nConstraints: z != 0\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.2#E2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=ln"
}
}
}
},
"positions" : [ {
"section" : 1,
"sentence" : 0,
"word" : 19
} ],
"includes" : [ "x", "x)" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "integral representation",
"score" : 0.6859086196238077
}, {
"definition" : "positive real number",
"score" : 0.6859086196238077
}, {
"definition" : "logarithmic integral",
"score" : 0.5988174995334326
} ]
}